Dayside ionosphere of Titan: Impact on calculated plasma densities due to variations in the model parameters

Dayside ionosphere of Titan: Impact on calculated plasma densities due to variations in the model parameters

Accepted Manuscript Dayside ionosphere of Titan : Impact on calculated plasma densities due to variations in the model parameters Vrinda Mukundan, An...

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Accepted Manuscript

Dayside ionosphere of Titan : Impact on calculated plasma densities due to variations in the model parameters Vrinda Mukundan, Anil Bhardwaj PII: DOI: Reference:

S0019-1035(16)30849-1 10.1016/j.icarus.2017.07.022 YICAR 12543

To appear in:

Icarus

Received date: Revised date: Accepted date:

24 December 2016 13 July 2017 31 July 2017

Please cite this article as: Vrinda Mukundan, Anil Bhardwaj, Dayside ionosphere of Titan : Impact on calculated plasma densities due to variations in the model parameters, Icarus (2017), doi: 10.1016/j.icarus.2017.07.022

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Highlights • A one dimensional photochemical model is developed for the calculation of density of ions and electron in the dayside ionosphere of Titan.

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• The calculated electron density is about a factor of 2 to 3 larger than the Cassini measurement. • A detailed assessment of the model parameters affecting the production and loss of ions is conducted.

• Model calculations suggest that a more significant role is played by the loss processes, rather than the production processes, in causing the disagreement between modeled and observed

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electron density.

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Dayside ionosphere of Titan : Impact on calculated plasma densities due to variations in the model parameters Vrinda Mukundan1∗, Anil Bhardwaj1,2 1 Space

Physics Laboratory, Vikram Sarabhai Space Centre, Trivandrum-695022, India Research Laboratory Ahmedabad-380009, India

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2 Physical

Abstract

A one dimensional photochemical model for the dayside ionosphere of Titan has been developed for

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calculating the density profiles of ions and electrons under steady state photochemical equilibrium condition. We concentrated on the T40 flyby of Cassini orbiter and used the in-situ measurements from instruments onboard Cassini as input to the model. An energy deposition model is employed for calculating the attenuated photon flux and photoelectron flux at different altitudes in Titan’s ionosphere. We used the Analytical Yield Spectrum approach for calculating the photoelectron + + + fluxes. Volume production rates of major primary ions, like, N+ 2 , N , CH4 , CH3 , etc due to photon

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and photoelectron impact are calculated and used as input to the model. The modeled profiles are compared with the Cassini Ion Neutral Mass Spectrometer (INMS) and Langmuir Probe (LP)

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measurements. The calculated electron density is higher than the observation by a factor of 2 to 3 around the peak. We studied the impact of different model parameters, viz. photoelectron flux, ion production rates, electron temperature, dissociative recombination rate coefficients, neutral

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densities of minor species, and solar flux on the calculated electron density to understand the possible reasons for this discrepancy. Recent studies have shown that there is an overestimation in the modeled photoelectron flux and N+ 2 ion production rates which may contribute towards this

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disagreement. But decreasing the photoelectron flux (by a factor of 3) and N+ 2 ion production rate (by a factor of 2) decreases the electron density only by 10 to 20%. Reduction in the measured

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electron temperature by a factor of 5 provides a good agreement between the modeled and observed electron density. The change in HCN and NH3 densities affects the calculated densities of the major ∗ Corresponding

author: Phone: +91 471 2563663 Email addresses: [email protected], [email protected] (Vrinda Mukundan1 ), [email protected], [email protected] ( Anil Bhardwaj1,2 )

Preprint submitted to Icarus

August 4, 2017

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+ ions (HCNH+ , C2 H+ 5 , and CH5 ); however the overall impact on electron density is not appreciable

(<20 %). Even though increasing the dissociative recombination rate coefficients of the ions C2 H+ 5 and CH+ 5 by a factor of 10 reduces the difference between modeled and observed densities of the major ions, the modeled electron density is still higher than the observation by ∼60% at the peak. additional loss of plasma in Titan’s ionosphere. Keywords: Titan, atmosphere, photochemistry, ionosphere

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We suggest that there might be some unidentified chemical reactions that may account for the

Upper atmosphere of Titan hosts a very complex ionospheric chemistry scheme. The major

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neutral atmospheric constituents of this Saturnian moon are N2 (∼95%) and CH4 (∼4%) (M¨ uller-

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Wodarg et al., 2012). When solar photons and other energetic particles collide with the neutrals

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+ + causing their photoionization or photodissociation, a suit of ions and radicals, like N+ 2 , CH4 , CH3 ,

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CH3 , etc. are formed. These products then start reacting with the background gases, thus initiating

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a chain of chemical reactions which ultimately result in the formation of heavy hydrocarbon ions

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and neutrals along with free electrons (Yung et al., 1984; Fox and Yelle, 1997; Wahlund et al.,

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2009). The in-situ measurements of Titan’s ionosphere made by Cassini spacecraft over the past

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decade have largely improved our understanding about the intricate chemistry happening in Titan’s

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ionosphere. However, the density of ions and electron calculated using different models are found to

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be higher (Robertson et al., 2009; Westlake et al., 2012) than the observations made by instruments

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onboard Cassini, viz. the Ion Neutral Mass Spectrometer (INMS), and Langmuir Probe (LP) which

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is a part of Radio and Plasma Wave Science (RPWS) experiment.

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There are many models which tried to address this disagreement between the calculated and

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observed electron density profiles. Westlake et al. (2012) presented a study using a one dimensional

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photochemical model and an empirical model of Titan’s dayside ionosphere constrained by Cassini

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measurements. They found that the major ion HCNH+ is overproduced in both empirical and

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photochemical model which would affect the electron density calculation. They proposed two new

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theoretical reactions for HCNH+ interactions with the neutrals C2 H2 and C2 H4 , each having a

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reaction rate coefficient of 2 x 10−10 cm3 s−1 , that can cause the loss of HCNH+ . Vigren et al.

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(2013) calculated the electron production rate using a solar energy deposition model, and combining

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this with an effective recombination rate coefficient and electron temperature (Te ) measured using

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LP, they predicted the electron densities that were a factor 2 higher than the observed densities.

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Vigren et al. (2013) concluded that there may be some unidentified loss process of free electrons

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other than dissociative recombination. Richard et al. (2015) also had a similar conclusion that

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over-abundance of electrons calculated by models is not due to over-production but due to unac-

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counted loss processes. Richard et al. (2015) compared the ion production rate calculated using a

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photochemical model with empirical production rates obtained using the ion densities measured by

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INMS and showed that there is good agreement between the two rates. The photochemical model

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of Dobrijevic et al. (2016), which included the coupling between the neutral and ionic species from

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the lower atmosphere up to the ionosphere, also over-predicted the electron number densities.

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Various factors can contribute towards this difference between calculated and measured electron

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density profile. The current paper aims at investigating the model parameters, viz. photoelectron

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flux, ion production rate, electron temperature, reactions and rate coefficients, neutral densities, and

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solar flux models whose variations can affect the calculated electron density. With this objective,

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we have developed a one dimensional photochemical model of the dayside ionosphere of Titan. The

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Analytical Yield Spectrum (AYS) technique is used to calculate the steady state photoelectron

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flux. These photoelectrons, along with solar photons, are taken as the major source of ionization.

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The densities of major ions and electron obtained using the model are compared with the Cassini

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INMS and RPWS/LP observations and also with the calculations of other models. We focus on

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the Cassini T40 flyby of Titan that occurred on 5 January 2008 which is a complete dayside flyby,

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having a solar zenith angle of 37.2o and for which measured electron and ion density profiles are

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available. We have also made calculations for few other Titan flyby conditions and compared with

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the observations.

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1. Model description

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The rate of change of number density, ni , of the ith ion species is given by the continuity equation

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dni + 5.φi = Pi − Li dt

(1)

where Pi and Li are the production and loss rate of the ion per unit volume, and 5.φi represents

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the flux divergence due to ion transport. Under steady state condition, and in the photochemical

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equilibrium region, where the transport processes are not important, the continuity equation reduces

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to

Pi = Li 4

(2)

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This continuity equation is solved for each ion species at each altitude independently for calculating

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the densities. The photochemical equilibrium prevails in Titan’s atmosphere at altitudes below 1400

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km (Ma et al., 2006; Cui et al., 2010) and the major sources of ionization in the dayside ionosphere

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are solar photons and photoelectrons (Galand et al., 2010). Our methodology is same as that adopted by Keller et al. (1992) and Keller et al. (1998) who

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have developed a one dimensional photochemical model for studying the composition and density

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structure of Titan’s ionosphere. An energy deposition model is developed which describes the

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absorption of solar UV radiation using Beer Lambert law. The initial inputs to the model are

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solar UV radiation reaching at the top of the atmosphere, the altitudinal distribution of the neutral

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constituents, and the photoabsoption cross sections. The attenuated solar flux, thus obtained is

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used for calculating photoelectron production rate, which is subsequently used in the calculation

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of steady state photoelectron flux by employing an Analytical Yield Spectrum (AYS) approach

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which is based on Monte Carlo simulations (Bhardwaj and Michael, 1999; Bhardwaj and Singhal,

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1993; Bhardwaj and Jain, 2012; Bhardwaj and Mukundan, 2015; Mukundan and Bhardwaj, 2016).

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+ + Primary production rate or the volume ionization rate of major primary ions, like N+ 2 , CH4 , CH3 ,

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etc., due to photon as well as photoelectron impact are calculated. The ion production rate is

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used as input to a photochemical model which includes ion-neutral chemistry. The production and

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destruction reactions of various ions are taken in the model to calculate the number density of

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different ionic species and electron.

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2. Model Inputs

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2.1. Solar flux

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The solar extreme ultraviolet (EUV) flux is taken from High resolution EUV flux for Aeronom-

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ical Calculations (HEUVAC) model (Richards et al., 2005). We have used the solar flux in the

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wavelength range 5 to 1055 ˚ A for the date 5 January 2008, with an F10.7 value of 77.1 and the

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Fav 10.7 value of 69.4 (Westlake et al., 2012) with a bin resolution of 10 ˚ A. The flux is reduced by

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1/r2 , where r is the mean Sun-Titan distance which is 9.5 AU.

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2.2. Neutral densities

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The density profiles of the major atmospheric species N2 , CH4 and H2 are taken from Mandt

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et al. (2012) which are simulated using an ion neutral thermal model for the conditions relevant for 5

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the T40 flyby. These densities are in good agreement with the neutral densities measured by INMS.

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In addition to the major constituents, the photochemical model requires the density profiles of the

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minor atmospheric species as well. Following the methodology of Richard et al. (2015), we have

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used the mixing ratio profiles of 14 minor species given by Krasnopolsky (2009) (except for CH2 NH

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which is taken from Lavvas et al. (2008)) after shifting the profiles to make them consistent with

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the global average mixing ratios as given by Magee et al. (2009), Cui et al. (2009) and Robertson

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et al. (2009) (see Table 1 of Richard et al. (2015)).

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2.3. Cross sections

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Cross sections of the major atmospheric constituents due to photon and electron impact are

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important inputs for calculating the attenuated solar flux and photoelectron flux in Titan’s upper

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atmosphere. Photoabsorption and photoionization cross sections of N2 and CH4 used in the model

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are the same as that in Bhardwaj and Jain (2012) in which photo-cross sections are taken from the

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database http://amop.space.swri.edu (Huebner et al., 1992). Photo cross sections for the H+ 2 and

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C+ production channels of CH4 are taken from Lavvas et al. (2011). Inelastic cross sections for the

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electron impact on N2 are taken from Bhardwaj and Jain (2012). For CH4 , analytically fitted form

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of electron impact cross sections as given by Bhardwaj and Mukundan (2015) are used.

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2.4. Reaction rate coefficients

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The reaction rate coefficients for the various ion-neutral reactions used in the model are pri-

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marily based on McEwan and Anicich (2007) and Vuitton et al. (2007). The dissociative electron

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recombination coefficients and the temperature dependent factors are from Richard (2013).

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2.5. Electron temperature

The electron temperature is required for calculating the loss rate of various ions via electron

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recombination reaction. For obtaining the electron temperature at each altitude, we have used the

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linear relation given by Dobrijevic et al. (2016) as

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Te (Z) = (1/0.715)(Z − 642.5)

(3)

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where Z is the altitude in km. This linear relationship matches well with the RPWS/LP measured

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electron temperature during T40 flyby (see section 7.3).

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3. Photoelectron production rate Photoelectron production rate at an altitude Z is calculated using Q(Z, E) =

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nl (Z)

l

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σlion (j, λ) I(Z, λ)

(4)

j,λ

Here nl (Z) is the density of the neutral constituent l at altitude Z, σlion (j, λ) is the photoionization

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cross section of the j th ionization state of the lth constituent at wavelength λ and I(Z, λ) is the

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solar flux of wavelength λ at altitude Z which is calculated as I(Z, λ) = I(∞, λ) exp[−τ ]

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where

σla (λ)

Z



(5)

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nl (Z )dZ ,

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τ (λ, Z) = sec(χ)

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l

(6)

Z

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is the optical depth at wavelength λ and altitude Z, σla is the total photoabsorption cross section of

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the constituent l at λ, I(∞, λ) is the unattenuated solar flux at λ reaching the top of the atmosphere

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and χ is the solar zenith angle (SZA). Figure 1 shows the calculated photoelectron production rate

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for three different altitudes, for SZA of 37o . The sharp peak at ∼24 eV is due to the ionization of N2 by intense solar He II lines at 303.8 ˚ A. Photoelectrons of energy >50 eV is more at lower

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altitudes as these high energy photoelectrons are produced by solar photons with wavelength <200

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˚ A which can penetrate deeper into the atmosphere. However, low energy electrons (<30 eV) are

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more at higher altitudes as they are produced by photons of λ > 275 ˚ A whose altitude of unit

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optical depth is above 1000 km.

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4. Photoelectron flux

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The primary photoelectrons generated in the atmosphere during photoionization loose their

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energy by colliding with the background neutrals. Using the Analytical Yield Spectrum (AYS)

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approach, we calculate the degraded electron spectrum. Yield spectrum, U(E, E0 ) of any gas,

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for an incident electron energy E0 , is defined as the number of discrete energy loss events that

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happened when the spectral energy of the electron is between E and E+∆E.

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U (E, E0 ) =

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N (E) , 4E

(7)

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where N(E) is the number of inelastic collisions and 4E is the energy bin width which is 1 eV in

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our model. It is obtained as the output of a Monte Carlo simulation for the energy degradation of

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monoenergetic electrons in gases (Green et al., 1977; Singhal et al., 1983; Bhardwaj and Michael,

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1999; Bhardwaj and Jain, 2009; Bhardwaj and Mukundan, 2015). The yield spectrum of a mixture

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of gases, called composite yield spectrum is obtained as: Uc (E, E◦ ) =

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X l

fl Ul (E, E◦ )

where ρl n l fl = P l ρl n l

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(8)

(9)

Here Ul (E, E◦ ) is the yield spectrum for individual gases, nl is the number density of lth gas, and

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ρl is the average value of the total inelastic cross section of the lth gas between E and E0 . As the

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most abundant gases in the atmosphere of Titan are N2 and CH4 , the yield spectrum of these gases

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are required to calculate the composite yield spectrum. For N2 , we have used the AYS given by

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Singhal et al. (1980) as :

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U (E, E0 ) = C0 + C1 Ek + C2 Ek2 where

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(E0 /1000)Ω E+L

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Ek =

(10)

(11)

C0 , C1 , C2 , Ω and L are the fitted parameters which are independent of the energy. For CH4 , the AYS is taken from Bhardwaj and Mukundan (2015), which is given as

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U (E, E0 ) = A1 ξ0s + A2 (ξ01−t /3/2+r ) +

E0 A0 e−A5 x /A3 (1 + eA6 x )2

(12)

Here x = (E − A4 )/A3 , and A0 , A1 , A2 , A3 , A4 , A5 and A6 are the fitting parameters. Using

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equations (10) and (12), we calculated the composite yield spectrum using equation (9). Once the composite yield spectrum is obtained, photoelectron flux is calculated as: Z 500 Q(Z, E) Uc (E, E0 ) X ψ(Z, E) = dE0 E nl (Z) σl (E)

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(13)

l

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Here Q(Z, E) is the photoelectron production rate at altitude Z which is calculated using equation

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(4). Figure 2 shows the calculated photoelectron flux for three different altitudes. For all altitudes, 8

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flux is maximum for electrons having energy <10 eV. The peak at ∼24 eV, which occurs due to the

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ionization of N2 by He II line, is seen in the degraded spectrum as well. At 900 km, this peak seems

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to be absent which indicates that the He II photons at 303 ˚ A get absorbed at higher altitudes.

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The decrease in the flux of photoelectrons having energy >50 eV is due to the corresponding

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decrease in the production rate of these high energy photoelectrons. This is caused by the drop

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in the solar EUV flux and the ionization cross sections at shorter wavelengths. Figure 3 shows

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a comparison of the photoelectron flux calculated using the current model with that of Cassini

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Plasma Spectrometer-Electron Spectrometer (CAPS-ELS) observations and previous models. Our

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calculated flux is consistent with the calculations of Lavvas et al. (2011) and Richard et al. (2015).

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The measured photoelectron flux peaks at an energy slightly lower than the modeled values. Lavvas

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et al. (2011) pointed out that this occurs due to the low value of the spacecraft potential (-0.5 V) used

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in the retrieval of photoelectron flux from CAPS/ELS observation. Lavvas et al. (2011) suggested

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a higher value of -1.2 eV for the spacecraft potential based on the location of He II peak. If the

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CAPS/ELS observations are shifted by 1.2 eV to account for the spacecraft potential during the

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time of measurement, there is a better agreement between the peak of the modeled and measured

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photoelectron flux.

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5. Volume Production Rates

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The primary production rate of an ion species i at an altitude Z is given by Z Vi (Z) = nl (Z) ϕ(Z, E) σil (E) dE

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(14)

where nl (Z) is the density of the parent neutral species, ϕ(Z, E) is the photon/photoelectron flux at

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the altitude Z and energy E, and σil is the photoionization/electron impact ionization cross section

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for ion species i being produced from neutral species l at energy E.

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Figure 4 shows the primary production rate of various ions. For the major primary ion N+ 2,

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the maximum production rate (15 cm−3 s−1 ) occurs at an altitude of ∼1040 km. Whereas for

N+ , the peak production (2 cm−3 s−1 ) occurs at lower altitudes (∼980 km) because the higher

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energy photons that are required to cause the dissociative ionization of N2 can penetrate to these

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−3 −1 altitudes. The CH+ s 4 production rate profile shows a flattened peak with a value of ∼0.4 cm

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between 850 km and 1000 km, a feature which is also seen in the calculated production rate profile

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of Richard et al. (2015) and Lavvas et al. (2011). This is because molecular nitrogen does not 9

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absorb much photons having wavelength ∼900 ˚ A, the wavelength region where CH+ 4 production

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has maximum cross section. This allows more photons with energy near the ionization threshold

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of CH4 to penetrate deeper in to the atmosphere and produce an extended peak (Richard, 2013).

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−3 −1 For CH+ s ) occurs at around 1030 km. For the minor ions, viz. 3 , the peak production (0.2 cm

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+ + + + CH+ 2 , CH , C , H2 , and H , which are produced through the dissociative ionization of methane

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by photon/photoelectron impact, the altitude of peak production occurs at 1036 km, 1009 km,

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1009 km, 1011 km, and 1014 km with the peak values 0.02, 0.008, 0.001, 0.001, and 0.01 cm−3 s−1 ,

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respectively.

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+ + In Figure 5, we have compared the production rates of major primary ions N+ 2 , N , CH4 and

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o CH+ 3 with the calculations of Lavvas et al. (2011) and Richard et al. (2015) for a SZA of 60 . For

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−3 −1 N+ s occurs at ∼1065 km which is consistent with the calculations 2 , the peak value of 9 cm

of Richard (2013) who obtained a value of 8 cm−3 s−1 at ∼1070 km, whereas Lavvas et al. (2011)

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obtained a value of 5 cm−3 s−1 at the same altitude. The secondary peak at ∼900 km occurs due

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to the ionization caused by x-ray photons and photoelectrons having energy >100 eV, which is

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seen in all three profiles. Similarly for N+ , the peak value calculated by Lavvas et al. (2011) and

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Richard (2013) (1.4 cm−3 s−1 ) are ∼40% higher than that of the current model. The altitude of

peak production for N+ is also slightly low as compared to the altitudes obtained by the other two

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+ models. The difference between the production rate values of N+ calculated by Lavvas 2 and N

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et al. (2011), Richard et al. (2015) and the present study is mainly caused by the difference in the

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photoionization cross sections of N2 . The photo cross sections for N+ 2 production that we have

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used is around 10 to 20% higher than that of Lavvas et al. (2011) in the wavelength range 200-600

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˚ A whereas as, those used by Richard et al. (2015) are in good agreement with our values. For

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N+ , our photo cross sections are lower than that of Lavvas et al. (2011) and Richard et al. (2015)

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to a maximum of one order of magnitude at few energies. For the major ionization products of

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+ methane, viz. CH+ 4 and CH3 , the difference between our calculated peak values and that of Lavvas

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et al. (2011) and Richard (2013) is less than 20%. The higher value for the CH+ 4 production rate

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of Lavvas et al. (2011) is due to the use of high resolution photoabsorption cross sections of N2 in

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the wavelength range 840-1000 ˚ A (The impact of high resolution photoabsorption cross sections of

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N2 on the calculated volume production rates is discussed in the following section). Overall, our

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calculations are in agreement with the volume production rates calculated by models of Richard

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(2013) and Lavvas et al. (2011).

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5.1. Impact of high resolution N2 photo cross sections on volume production rate calculations Many recent studies recommended the use of high resolution (HR) photoabsorption cross sections

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of N2 in the wavelength range 845-1000 ˚ A for the meticulous calculation of volume production rates

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(Lavvas et al., 2011; Mandt et al., 2012; Sagnieres et al., 2015). Photons in this wavelength range

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are capable of ionizing CH4 (whose ionization threshold is 945 ˚ A or 13.12 eV) but have energies less

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than the ionization threshold of N2 (796 ˚ A or 15.57 eV). The fine structure of the HR cross sections

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of N2 allows more photons in this wavelength region to pass through the atmosphere without getting

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absorbed by N2 . This enhances the ionization rate of CH4 at lower altitudes as compared to case

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when low resolution cross sections are used.

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To asses the impact of HR cross sections on our production rate calculations, we ran the model

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using the HR cross sections derived by Liang et al. (2007) for the wavelength 840-1000 ˚ A. We

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averaged these cross sections into 0.1 ˚ A bins with appropriate solar flux taken from HEUVAC

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model. The use of HR cross sections does not have any effect on the production rate of N+ 2 and

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+ N+ . However enhancement in the CH+ 4 and CH3 production rates are observed at altitudes below

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∼1000 km as can be seen from the Figure 6(a). Figure 6(b) shows a comparison between the CH+ 4

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production rates calculated using the low resolution (LR) and HR photoabsorption cross sections

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of N2 by Lavvas et al. (2011) and the current model for a SZA of 60o It can be seen that there

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is a closer match between our LR and HR profiles as compared to the profiles by Lavvas et al.

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(2011). This occurs due to the difference in the LR mode photo cross sections adapted. Lavvas

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et al. (2011) have used the N2 photoabsorption cross sections of Samson et al. (1987) where as we

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use the photo cross sections by Huebner et al. (1992), the bin resolution being 10 ˚ A in both studies.

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A comparison between these two cross sections, convolved into 10 ˚ A bins, is shown in the Figure

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6(c). The fine structures in the HR photoabsorption cross sections of N2 are better represented by

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the LR mode 10 ˚ A bin cross sections that we use as compared to the one used by Lavvas et al.

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(2011). This explains the reason for the better match between our LR and HR profiles.

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As we are calculating the plasma density profiles for altitudes above 1000 km, the region where

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the LR mode production rate values are consistent with those obtained in the HR mode, we continue using the volume production rates obtained in the LR mode itself for further calculations.

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Table 1: List of neutrals and ions included in the model

N2 , CH4 , H2 , N, C2 H2 , C2 H4 , NH3 C2 H6 , HCN, H, C4 H2 , HC3 N, C2 H3 CN,

+ + + + + + N+ 2 , N , CH4 , CH3 , CH2 , H2 , H ,

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CH3 CN, C3 H4 , C4 H2 , CH2 NH, C6 H6

+ + + + + HN+ 2 , CH5 , C2 H5 , CHCCNH , HCNH , HCN + + CH3 CNH+ , C3 H+ 5 , c-C3 H3 , C2 H3 CNH ,

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6. Photochemical equilibrium model

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+ + + + + NH+ 4 , CH3 NH3 , C4 H3 , C6 H5 , C6 H7 , CH2 NH2

To calculate the density profiles of the ion species, the primary production rates of various ions

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discussed in the previous section are used as input to the photochemical equilibrium model which

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includes the ion-neutral chemistry. Table 1 gives a list of neutral and ion species that have been

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+ included in our model. The dominant ions in Titan’s ionosphere are HCNH+ , C2 H+ 5 and CH5 .

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In the altitude range 1050-1200 km, HCNH+ constitutes about 40-50% of the total ion population

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+ measured by INMS. C2 H+ 5 and CH5 contributes ∼15% and ∼2%, respectively (Cravens et al., 2006;

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+ + + Westlake et al., 2012). These ions, along with other ion species, like CH+ 3 , CH2 NH2 , c-C3 H3 , C3 H5 ,

241

CH3 CNH+ , and CHCCNH+ , account for ∼80% of the INMS observed ion population (Vigren et al.,

242

2013).

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The calculated density profiles of the three major ions in Titan’s ionosphere, HCNH+ , C2 H+ 5

244

and CH+ 5 for the T40 flyby conditions are shown in Figure 7 along with those calculated by other

245

+ photochemical models. The peak densities for HCNH+ , C2 H+ 5 and CH5 calculated using our model

246

is higher than the corresponding INMS observed densities by factor of two to six. The HCNH+

247

profile shows a good match with the profile of Westlake et al. (2012) at regions >1200 km. However,

248

there is ∼30 km difference between altitude of peak production and our peak value is ∼40% higher

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249

than that of Westlake et al. (2012). Profile of Dobrijevic et al. (2016) shows closest match with

250

the observations as they have included the reaction N(2 D) + HCN → CH + N2 which consumes

251

HCN thus lowering the production of HCNH+ , that is not included in any other model including

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Flyby

Date

SZA

T40

5 January 2008

37

T48

5 December 2008

25.3

T86

26 September 2012

46.4

T95

14 October 2013

25

T104

21 August 2014

12.1

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Table 2: Information on the Cassini flybys used in our study

252

+ the current model. For C2 H+ 5 and CH5 , the general shape of our profiles matches with those of

253

Westlake et al. (2012) and Dobrijevic et al. (2016), but our calculated values are slightly higher. Figure 8 shows the density profiles of 20 other ions calculated using our photochemical model.

255

Densities of all the 23 ions are then added to calculate the total electron density at each altitude.

256

The electron density profile thus obtained is shown in Figure 9 along with the RPWS/LP measured

257

electron density and calculations of other models (Westlake et al., 2012; Vigren et al., 2013; Dobri-

258

jevic et al., 2016). The calculated density profile is found to be consistent with other model results,

259

even though our calculated altitude of peak production is slightly lower (∼1050 km) as compared to

260

other models. This is due to the difference in the calibration constant adopted by different models

261

with which the neutral densities measured by INMS are multiplied to account for the recalibration

262

of the instrument. Westlake et al. (2012) and Vigren et al. (2013) used a calibration factor of 3.0,

263

whereas we adopted a value of 2.2 based on the recent study of Teolis et al. (2015). A lower value

264

for the calibration factor slenderize the atmosphere, thus allowing the UV radiation to penetrate

265

to lower altitudes.

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Our calculated peak value of electron density is around a factor of 2.5 higher than the observa-

267

tion. All the models are overestimating the electron density by a factor of two to three. We modeled

268

the electron density profile for four more dayside Titan flybys, T48, T86, T95 and T104 (see Figure

269

10). Details of all the five flybys that are considered in our study are given in Table 2. For all

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the flybys, our modeled electron density profiles are consistently higher than the measured values

271

by a factor of 2 to 3. In the following section we explore the possible reasons that can contribute

272

towards this overabundance.

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274

7. Impact of model input parameters on the calculated ion and electron densities Electron density profile obtained using parameters described in section 2 will be hereafter referred to as standard case.

276

7.1. Impact of photoelectron flux

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On the dayside ionosphere of Titan, the main ionization sources are solar EUV photons and

278

solar EUV-generated photoelectrons. Any overestimation in the photon flux or photoelectron flux

279

will cause an aberrance in the value of ion production rates which will ultimately affect the electron

280

density. Recently, Vigren et al. (2016) showed that the model derived photoelectron fluxes are

281

higher than those measured by CAPS/ELS by a factor of ∼3±1 at electron energies less than 60

282

eV and suggested that this can be a probable reason for the higher electron densities predicted by

283

the models. However, our calculated photoelectron flux are consistent with the model calculations

284

of Richard et al. (2015) and Lavvas et al. (2011) as well as with the observations of CAPS/ELS

285

at an altitude of 1020 km (see Figure 3). Vigren et al. (2016) pointed out that the better match

286

of Richard et al. (2015) and Lavvas et al. (2011) calculations with the observation is due to the

287

fact that they have used the photoelectron fluxes measured by the central anode of CAPS/ELS

288

instrument for comparing with their calculations. The central anode CAPS/ELS measurements are

289

found to be higher than those measured by the anode 2 of the same instrument which Vigren et al.

290

(2016) have used in their study. However, this inconsistency in the measurement made by the two

291

different anodes is seen only at altitude close to 1021 km. At higher altitudes, viz. 1056, 1121 and

292

1201 km, the measurements by central anodes match with the anode 2 measurements (differing

293

only by <20% for the egress of T40 flyby).

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We compared our calculated photoelectron flux with the calculation of Vigren et al. (2016) and

295

the observation of CAPS/ELS (as given by Vigren et al. 2016) at an altitude of 1074 km. Our

296

calculations are higher than the observation by a factor of ∼2 to 3 at electron energies <60 eV

297

(see Figure 11). Vigren et al. (2016) calculated the electron impact production rates using modeled

298

photoelectron flux as well as using CAPS/ELS observed photoelectron flux at different altitudes

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299

for the dayside flybys T40, T41, T42 and T48. They used SEE/TIMED solar flux and adopted

300

a calibration factor of 2.9 for the INMS measured neutral densities for their calculation. Vigren

301

et al. (2016) found that the ratio of the ion production rates calculated using modeled fluxes to

302

the one obtained using observed fluxes has a value of ∼3.0 for electron energy less than 60 eV. A 14

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comparison of our calculated electron impact ion production rates with that of the ion production

304

rates calculated by Vigren et al. (2016) using the observed photoelectron fluxes also showed a similar

305

result. To understand the effect of this over-estimation of photoelectron flux on the plasma density

307

calculation, we reduced the photoelectron flux by a factor of 3. Figure 12(a) shows the electron

308

+ + + impact volume production rates of the major primary ions, N+ 2 , N , CH4 , and CH3 , obtained when

309

the photoelectron flux is reduced by a factor of 3. The peak production rate of all the four ions

310

is reduced by 60-70%. However, the electron impact ion production rates constitutes only ∼30%

311

of the total volume production rates (see Figure 12(b)). Decreasing the photoelectron flux reduces

312

this contribution to 15% and the total ion production rate is reduced by 20%. These modified ion

313

production rates are used for calculating the electron and ion densities. It is found that reducing

314

the photoelectron flux reduces the peak densities of major ions only by 10-15% and peak electron

315

density by ∼10% (see Figure 13). This shows that an overestimation in photoelectron fluxes may

316

not be an important factor in causing aberrance in the modeled electron density.

317

7.2. N+ 2 ion production rates

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A recent study of Sagni`eres et al. (2015) showed that the primary production rate of N+ 2 cal-

319

culated using solar energy deposition (SED) models are higher than the one which are derived

320

empirically using INMS measured ion and neutral densities by a factor of two. To check whether

321

the empirical volume production rates of N+ 2 could reduce the calculated plasma density, we made

322

test runs of the model using the empirical N+ 2 production rates of Madanian et al. (2016). These

323

values are chosen over the empirical values of Richard et al. (2015) and Sagni`eres et al. (2015) as the

324

former study uses the most recent INMS calibration factor for ion and neutral densities, based on

325

the study of Teolis et al. (2015), which we have also adopted for the present work. Figure 14 shows

326

a comparison between the production rate calculation of Madanian et al. (2016) and Sagni`eres

327

et al. (2015). The maximum difference of a factor of ∼1.5 between the SED and empirical values

328

of Sagni`eres et al. (2015) is occurring at an altitude of ∼1080 km. Our model calculated values are

329

in close agreement with the SED values of Madanian et al. (2016), with a difference less than 12%

330

at the peak. A ratio between our model calculated values and the empirical values of Madanian

331

et al. (2016) for different altitudes is presented in Table 3. It is evident that in the altitude range

332

1050-1100 km (the altitude region where the electron density peaks) the model calculated values

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are around a factor of ∼2 higher than the empirical values. We adjusted our calculated volume production rate of N+ 2 in such a way that it matches with the empirical values of Madanian et al.

335

(2016) (see Figure 14). These reduced N+ 2 ion production rates are used in the chemistry model.

336

The density profiles of major ions and electrons thus obtained is shown in Figure 15. The peak

337

+ density of electron and HCNH+ is decreased by 20% and that of CH+ 5 and C2 H5 is reduced by

338

∼30%. This shows that, even though the over-estimation of ion production rate is contributing

339

to the exaggerated plasma density to some extent, this alone is not sufficient to account for the

340

inconsistency between the observed and modeled electron density profiles.

341

7.3. Electron Temperature

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Dissociative ion-electron recombination reaction plays a major role in the loss of electrons and

343

ions. This reaction depends on electron temperatures (Te ). Higher the value of Te , lower will be

344

the rate of recombination, and hence higher will be the electron density. Theoretical studies suggest

345

that Te should be close to neutral temperature at altitudes below 1050 km (Richard et al., 2011).

346

However, observations revealed that Te is higher than the modeled values. Richard et al. (2011)

347

modeled dayside electron temperature for the T18 flyby condition for different magnetic topologies.

348

These modeled values were found to be smaller than that of the LP measurements. The magnitude

349

of difference depends on the magnetic topology that is considered in each case. Lavvas et al. (2013)

350

assumed a temperature profile for T40 which conciliate with both observations and theory. Modeled

351

Te for the outbound conditions of T40 flyby is given by Richard (2013). Figure 16(a) shows each

352

of these profiles along with the RPWS/LP observations for T40 and the linear relation for Te given

353

by Dobrijevic et al. (2016) which we have used in the standard case. We ran the model with each of

354

these Te profiles, keeping all other parameters the same as that in the standard case. Three cases

355

were considered.

356

Case 1 : Te modeled for T40 outbound from Richard (2013)

357

Case 2 : Te from Lavvas et al. (2013)

358

Case 3 : Te from Richard et al. (2011). We have extrapolated the Te profile of Richard et al.

359

(2011), taken from Westlake et al. (2012), for 1060 to 1000 km.

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Figure 16(b) shows the electron densities obtained in each case. All profiles agree with each

361

other for altitudes above 1250 km. The profile obtained in case 1 coincides with the standard case

362

profile at heights greater than 1200 km. However, the electron density peak is reduced by ∼15% 16

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Table 3: A comparison between empirically calculated production rate of N+ 2 by Madanian et al. (2016) and the values calculated using the present model

Altitude

Empirical Madanian et al. (2016) (cm

s

−1

Present model −3

)

(cm

−1

s

Ratio

)

8.43

14.27

1.69

1020

8.85

14.55

1.64

1024

7.51

14.68

1.96

1049

8.87

14.43

1.63

1056

8.09

14.08

1.74

1066

7.44

13.41

1.80

1076

6.92

12.60

1.82

1086

6.42

1097

5.85

1110

5.73

1124

5.27

1138

4.53

1152

3.89

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1.96

10.64

1.82

9.38

1.64

8.08

1.53

6.88

1.52

5.81

1.49

3.56

4.75

1.33

2.85

3.86

1.35

2.41

3.07

1.28

1.70

2.37

1.39

1.37

1.85

1.35

1257

0.95

1.42

1.50

1278

0.76

1.06

1.40

1298

0.58

0.80

1.37

1320

0.47

0.58

1.24

1343

0.36

0.42

1.17

1372

0.24

0.28

1.17

1397

0.19

0.20

1.01

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12.60

1168

1201 1220

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363

of the standard peak for ∼30% decrease in Te at 1050 km. The Te value at this altitude for the

364

case 2 and 3 profiles are, respectively, ∼60% and ∼70% less than that of the standard case profile.

365

Correspondingly, electron densities are reduced by ∼30% and ∼40%. Also, it is observed that when Te used in the standard case is reduced by a factor of 5, the

367

modeled electron density profile shows better agreement with the observed values at altitudes

368

>1150 km. Figure 17 shows the modeled electron density profile when the electron temperature is

369

reduced by a factor of 5 for the flybys, T48, T86, T95, and T105. At altitudes below ∼1050 km,

370

the modeled value is still higher than the observed value by ∼ 30-40% which suggests that Te has

371

to be still lower in this region for the calculated electron density to agree with the observation.

372

There is a possibility that the actual Te is less than the observed value in this region as Vigren

373

et al. (2013) has pointed out that it is difficult for the Langmuir probe to measure Te below 300 K

374

due to instrumental properties though the instrument is sensitive enough to measure Te less than

375

400 K.

376

7.4. HCN density

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In the photochemical model, HCN density is crucial for determining the density profiles of the

378

+ three major ions HCNH+ , C2 H+ 5 and CH5 as their densities are largely influenced by the reactions

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CH5+ + HCN → HCN H + (3.0 × 10−9 cm3 s−1 )

C2 H5+ + HCN → HCN H + (2.7 × 10−9 cm3 s−1 )

(15)

(16)

In the standard case we have used the mixing ratio profile of HCN given by Krasnopolsky (2009)

380

which was anchored to the mixing ratio reported by Magee et al. (2009) (see section 2.2). Recently,

381

Cui et al. (2016) derived the HCN abundance for the altitude range 960–1400 km by using the

382

INMS data obtained during several flybys of Titan. They also deduced an average dayside mixing

383

ratio profile for HCN. We have run the model by using different density profiles of HCN to see how

384

the electron and the major ion densities will vary in each case. Three different model runs were

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carried out:

386

Case 1 : HCN density measured during the inbound part of the T41 flyby (as given by Cui et

387

al. 2016) is fitted. (T41 flyby occurred on 22 February 2008 with a SZA of 30o , conditions which

388

are quite similar to T40.) 18

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389

Case 2 : Dayside average mixing ratio profile of HCN as given by Cui et al. (2016).

390

Case 3 : Reducing the density of HCN used in the standard case by a factor of 3.

391

Figure 18 shows the different HCN profiles that we have used for model runs. In case 1, the

393

HCN density is larger than that in the standard case at altitudes <1100 km but at higher altitudes

394

it is lower by a factor of ∼10 at the maximum. Correspondingly, the peak density of electron as well

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as HCNH+ is higher at altitudes <1100 km are lower than the standard profile at upper region (see

396

+ Figure 19). The observed effect is just opposite for C2 H+ 5 and CH5 . The maximum decrease in the

397

peak electron density occurs in case 3, i.e, when HCN density in the standard case is reduced by a

398

factor of 3. Decreasing the HCN density by a factor of 3 was suggested by Westlake et al. (2012)

399

in accordance with the uncertainties in the mixing ratio reported by Magee et al. (2009). The peak

400

electron density in this case is ∼10% less than the standard peak. There occurs a drastic decrease

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+ in the HCNH+ peak (by a factor of ∼1.75) but at the cost of C2 H+ 5 and CH5 density profiles which

402

is also suggested by Westlake et al. (2012). In case 2, the dayside average mixing ratio of HCN

403

reported by Cui et al. (2016) is ∼80% higher than that of the mixing ratio given by Magee et al.

404

(2009) at an altitude of 1050 km. However, using this dayside average profile causes a decrease in

405

+ the peak electron and HCNH+ densities with a reasonable shift in the C2 H+ 5 and CH5 profiles.

406

+ 7.5. Dissociative electron recombination coefficient (DRC) of C2 H+ 5 and CH5

M

401

Dissociative electron recombination reaction of ions is the major loss channel through which the

408

plasma is removed from the ionosphere. As shown in Figure 7, there is a large overestimation in

409

the densities of major ions which ultimately reflects as an over-valuation in the calculated electron

410

density. If the DRC for these ions were higher it would have caused the loss of these ions at a higher

411

−6 rate and hence a lesser value of electron density. For CH+ cm3 5 we have used a DRC of 1.1 x 10

412

s−1 (McLain et al., 2004). Several authors have reported different values, e.g., 2.9 x 10−7 cm3 s−1

413

(Sheehan and St.-Maurice, 2004), 7.0 x 10−7 cm3 s−1 (Lehfaoui et al., 1997), and 1.4 x 10−7 cm3

414

s−1 (Smith and Spanel, 1993). Similarly for C2 H+ 5 , the DRC value used in the standard case is 1.2

415

x 10−6 cm3 s−1 (McLain et al., 2004). For this ion also DRC has been reported by Lehfaoui et al.

416

(1997) (6.0 x 10−7 cm3 s−1 ) and Adams and Smith (1988) (7.4 x 10−7 cm3 s−1 ). It is evident that

417

there are considerable differences between various reported values of DRC.

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418

To reduce the densities of major ions and electron, we tried increasing the DRC of CH+ 5 and

19

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419

+ C2 H + 5 by keeping the DRC of HCNH same as that in the standard case. Increasing the DRC of

420

+ C2 H + 5 and CH5 simultaneously by a factor of 5(10) reduces the difference between the observations

421

+ and modeled profile from a factor 7 to a factor of 4(3) for CH+ 5 and from 7 to 3(2) for C2 H5 (see

422

Figure 20). The HCNH+ profile also got improved with the peak value in the standard case ∼3500 cm−3 reducing to 2500 cm−3 (∼2300 cm−3 ). The peak electron density also decreased to 5000

424

cm−3 (4500 cm−3 ) from the standard case peak of 6500 cm−3 . Even though increasing the DRC

425

improved the calculated densities, the modeled profiles are still higher than the observation which

426

suggests that there may be some chemical reactions involving the major ions HCNH+ , C2 H+ 5 and

427

CH+ 5 which are not identified so far that could account for the additional loss of these ions.

428

7.6. Additional reactions proposed by Westlake et al. (2012)

430

Westlake et al. (2012) proposed that there can be additional loss channels for HCNH+ that can

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consume the ion and reduce the density. They suggested the following loss reactions for HCNH+

431

HCN H + + C2 H2 → CHCCN H + + H2 (2.0 × 10−10 cm3 s−1 )

(17)

HCN H + + C2 H4 → C2 H3 CN H + (2.0 × 10−9 cm3 s−1 )

(18)

However, there was no experimental evidence that such reactions could exist. To test the impact

433

on the model results, we made a test run by including these two reaction. Figure 21 shows the

434

electron and HCNH+ density thus obtained in these case along with the standard case profile

435

and measured densities. New profiles agree with standard case profile at altitudes above 1250 km.

436

Inclusion of these reactions reduced the peak value of HCNH+ density by ∼30% and that of electron

437

density by ∼8%.

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Demarais et al. (2013) investigated the chemistry of HCNH+ with C2 H2 and C2 H4 using the

439

flowing afterglow-selected ion flow tube technique. They concluded that the large energy barriers

440

will inhibit these reaction pathways and they will not contribute significantly to the depletion of

441

HCNH+ and the suggested ionic products will not be formed from these reaction unless the energy

442

barrier is overcome.

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443

7.7. NH3 density

444

Our photochemical model overestimates the density of NH+ 4 ion by 2 orders of magnitude (see

445

Figure 22). Similar result was reported by Richard (2013) whose modeled NH+ 4 value was around a 20

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factor of 50 larger than the observation. The NH+ 3 density depends on the density of NH3 . Higher

447

the NH3 density, higher will be the abundance of NH+ 4 and vice versa. Yelle et al. (2010) and

448

Dobrijevic et al. (2016) modeled the density of NH3 by considering a coupled ion-neutral chemistry

449

scheme. Their profiles seem to be lower than that of our the standard case by a factor 75 and

450

20, respectively (see Figure 22). We ran the model using each of these density profiles to assess

451

how the NH+ 4 density varies. Using the profile of Dobrijevic et al. (2016) we could reduce the

452

difference between the model and observation to a factor of 10 or less. When the NH3 profile of

453

Yelle et al. (2010) is used, the agreement between observation and model further improved, reducing

454

the maximum difference from an order of magnitude to 60% at maximum. However, improving the

455

+ NH+ 4 density had a noticeable impact on HCNH density profile (and hence on electron density)

456

as reaction of HCNH+ with NH3 to form NH+ 4 is an important loss channel for this ion. Using the

457

NH3 profile from Yelle et al. (2010) or Dobrijevic et al. (2016) increased the peak value of HCNH+

458

(electron) by ∼33% (15%) of the standard case peak value.

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The sensitivity test of HCN and NH3 , presented in Section 7.4 and 7.7, respectively, suggests

460

the importance of these minor species in determining the densities of major ions HCNH+ , C2 H5+ ,

461

and CH+ 5 . However, due to coupled chemistry, the overall impact on the modeled electron density

462

is not appreciable as the decrease in the density of HCNH+ is compensated by the increase in the

463

density of C2 H5+ and CH+ 5 and vice versa.

464

7.8. Impact of Solar flux models

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To see how the model results vary with input solar flux models, we did test runs using different

466

solar flux models, viz. Solar2000 (S2K) model v.2.38 (Tobiska et al., 2000) and Solar EUV Exper-

467

iment (SEE, Version 11.0) (Woods et al., 2005). Figure 23 shows the solar EUV fluxes at 1 AU

468

generated using S2K and SEE for the day 5 January 2008 along with HEUVAC flux which we have

469

used in the standard case. It is seen that S2K and SEE fluxes are generally higher than that of the

470

+ + HEUVAC with noticeable difference in the wavelength range 30-70 nm where N+ 2 , CH4 and CH3

471

photoionization cross sections are high. Increased flux in this wavelength regime would cause higher

472

volume production rate leading to increased electron densities. Figure 24 shows electron density

473

profiles obtained by using different flux models. Profiles calculated using S2K and SEE match with

474

each other at altitudes above 1200 km. At the altitude of peak production (∼1050 km) the S2K

475

and SEE profiles are higher than that of the standard case profile by ∼17% and 10%, respectively.

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Overall, the difference between the standard case profile and profile obtained using SEE and S2K

477

is only ∼15%. This suggest that input solar flux model does not make any significant impact on

478

the electron density profiles.

479

8. Summary

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480

We have developed a one dimensional steady state model for the dayside ionosphere of Titan for

481

photochemical equilibrium condition. The calculated electron density profile in Titan’s ionosphere

482

is found to be larger than that measured by Cassini by a factor of 2 to 3 around the peak. We have

483

made a comprehensive assessment of various model parameters to understand their impact on the

484

calculated plasma densities.

Following the suggestion of Vigren et al. (2016), we reduced the model calculated photoelectron

486

flux by a factor of 3 to evaluate the impact of the exaggerated photoelectron flux on the calculated

487

plasma density. The peak electron density is found to decrease by only ∼10%. Use of the empirical

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production rate of N+ 2 ion, calculated by Madanian et al. (2016), also could make a difference of not

489

more than 20% in the peak electron density. Our model calculations suggest that the use of model

490

electron temperature profile, instead of the measured one, can improve the density calculations.

491

The electron temperature measured by Cassini RPWS/LP has to be reduced by a factor of 5 to

492

bring the modeled electron densities come closer to the LP observations. Even though increasing

493

+ the dissociative recombination rate coefficients of the ions C2 H+ 5 and CH5 by a factor of 10 could

494

+ + bring the calculated major ion densities (C2 H+ 5 , CH5 and HCNH ) closer to the observations, the

495

model electron densities are higher than the observation by ∼60% around the peak. The use of

496

different available density profiles of minor neutral species, HCN and NH3 , have noticeable impact

497

+ + on the profiles of C2 H+ 5 , CH5 and HCNH . However the decrease in the peak electron density is

498

<20% due to the coupled chemistry between these three ions. We show that the use of different

499

solar flux models (HEUVAC, SEE and S2K) can cause only about 15% change on the modeled

500

electron densities.

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The Cassini observed density profiles are consistent with model calculations when we varied the

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502

parameters which influence the loss of ions and electrons, viz. electron temperature and dissocia-

503

tive electron recombination rate coefficients. This shows that even though the over-estimation in

504

the production parameters, namely photoelectron flux and primary production rate of N+ 2 , may

505

contribute towards the disagreement between the modeled and observed plasma density profiles to 22

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some extent, a more significant role is played by the loss processes, in agreement with the study

507

of Richard et al. (2015), Westlake et al. (2012) and Vigren et al. (2013). It is probable that some

508

important chemical reactions are missing that may account for the additional loss of ions and

509

electrons.

510

Acknowledgments

511

512

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We thank, Hadi Madanian of University of Kansas, and Dr. Jun Cui of National Astronomical Observatories of China, for providing the INMS data on the neutral density profiles.

513

Vrinda Mukundan gratefully acknowledge ISRO for the research fellowship provided during the

515

period of this work.

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Figure 10: Calculated electron density profile for various Titan flybys compared with Cassini RPWS/LP observations.

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Figure 11: Calculated photoelectron flux at 1074 km compared with calculations of Vigren et al. (2016) and with Cassini CAPS observation (obtained from Vigren et al. (2016)). The dashed line indicates the case when the

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+ + + Figure 12: (a)Production rates of the major primary ions N+ 2 , N , CH4 , and CH3 due to electron impact. Solid lines show the electron impact

production rate obtained in the standard case and dashed lines shows the production rates obtained when photoelectron flux is reduced by a factor of 3.0 (b)Total ion production rates due to photon and photoelectron impact. Solid blue line shows the total ion production rates (photon + photoelectron) in the standard case and dashed red line shows the one obtained when the photoelectron flux is reduced by a factor of 3. Same is the case with the red lines which shows total ion production rates by electron impact.

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+ Figure 13: Density profiles of electron and the major ions, HCNH+ , C2 H+ 5 , and CH5 . Symbols show the Cassini observations. Solid red line is the profile

obtained in the standard case and dashed red line shows the calculated density when the photoelectron flux is reduced by a factor of 3.0.

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Figure 14: Comparison of volume production rate of N+ 2 calculated using the current study (solid red line) with that of Richard et al. (2015); Sagni` eres et al. (2015) and Madanian et al. (2016). Solid black lines and crosses shows the calculation of Sagni` eres et al. (2015), using solar energy deposition model (SED) model and empirical model,

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Figure 15:

+ Density profiles of electrons and major ions, HCNH+ , C2 H+ 5 , and CH5 , calculated using the em-

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pirical production rate of N+ 2 . Solid lines shows the standard case profiles. The dashed lines shows the profiles obtained when our calculated production rate values of N+ 2 are adjusted to match with the empirical calculations of Madanian et al. (2016).

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Figure 16: (a) Electron Temperature profiles used for testing model sensitivity. Circles and squares represents the Te measured by Langmuir probe during the T40 inbound and outbound conditions, respectively. Electron temperature of Richard et al. (2011) (from Westlake et al. (2012)) has been extrapolated from 1060-1000 km. Extrapolated region is represented by dotted line.(b) Electron density profile calculated using different electron temperatures profiles.

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Figure 17: Electron density profile calculated for the dayside flybys T48, T86, T95 and t104. Solid red lines shows the standard case profiles and blue dashed lines shows the profiles obtained when the RPWS/LP measured electron temperature is reduced by a factor of 5.0 for each flyby.

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Figure 18: HCN density profiles used for different model runs. Symbols represent the density measured by INMS

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+ Figure 19: Desity profiles of electron and major ions, HCNH+ , C2 H+ 5 and CH5 , obtained using different density profiles of HCN shown in Figure 18.Case 1 -

HCN density measured during the inbound part of the T41 flyby fitted linearly. Case 2 - Dayside average mixing ratio profile of HCN as given by Cui et al. (2016). Case 3 - Reducing the density of HCN used in standard case by a factor of 3.

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+ Figure 20: Density profiles of major ions and electron obtained by varying the dissociative recombination coefficient (DRC) of CH+ 5 and C2 H5 . Black circles

represents the INMS observations. Red solid line indicates the profile calculated in the standard case. Green dashed lines represents case 1 where the DRC of + + + CH+ 5 and C2 H5 increased by a factor 5. Blue dotted lines shows case 2 where the DRC of CH5 and C2 H5 increased by a factor 10.

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Figure 21: Density profiles of HCNH+ and electron obtained by adding theoretical reactions proposed by Westlake et al. (2012). Solid circles and open squares represent RPWS/LP measured electron density and INMS measured

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HCNH+ density, respectively. Red and blue lines show the calculated density profiles of electron and HCNH+ with solid lines representing the standard case profiles and dashed lines representing the profiles obtained when the

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Figure 22: NH3 densities used in the standard case along with the modeled profiles of Dobrijevic et al. (2016) (Case 1) and Yelle et al. (2010) (Case 2). NH+ 4 , HCNH+ , and electron density profiles obtained by using each of these profiles is also shown.

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